Capacitor Calculation for Buck Converter IC

Application Note

Switching Regulator IC series Capacitor Calculation for Buck converter IC

This application note explains the calculation of external capacitor value for buck converter IC circuit.

IN DD Buck converter I I

Figure 1 is the basic circuit of buck converter. 1 When switching element Q1 is ON, current ICIN Q flows from VIN through the coil L and charges ON IL L IO OFF the output smoothing capacitor CO, and the

output current IO is supplied. The current VIN CIN which flows into the coil L at this time induces ID ICO a magnetic field, and electric energy is D CO RL VOUT transformed into magnetic energy and accumulated for storage.

When switching element Q1 is OFF, free-

wheeling diode D turns ON and energy Current which flows at tON Current which flows at tOFF stored in L is then released to the output side. Figure 1. Basic buck converter circuit

Calculation of Input capacitor tON tON tON Q1 Rated voltage of input capacitor must be higher than the maximum input tOFF tOFF tOFF t voltage. Also rated ripple-current of the capacitor must be higher than the maximum input ripple-current of the IC. IO Although the average value of an input current becomes smaller in IDD proportion to the transformation ratio, momentarily the same current IIN t equal to output current flows through the buck converter as shown as IDD in Figure 2.

IO This will be averaged by the input capacitor, but as it is clearly shown as ID ICIN of Figure 2, the alternating ripple-current flowing in the input t capacitor, is higher than ICO of the output.

Effective value of ICIN can be calculated by following equation: IO ΔIL IL

푉푂푈푇 2 푉푂푈푇 1 2 t 퐼퐶퐼푁 = √ {퐼푂 (1 − ) + ∆퐼퐿 } [ARMS] (1) 푉퐼푁(푀퐼푁) 푉퐼푁(푀퐼푁) 12

Figure 3 shows the ripple heat generation characteristics of a ceramic ICO t capacitor (by Murata Manufacturing Co.). Whether it can be used as input capacitor or not is decided by this graph and the absolute maximum rating of ripple-current. ICIN t Be well aware of the temperature and DC bias impressed to the capacitor when using ceramic capacitor. Figure 2. Current waveform of each part

Change of capacitance value due to temperature can obtain stable temperature characteristic by using high permittivity ceramic capacitor with the characteristics of X5R and X7R.

Capacitance value reduces when DC bias at both sides of ceramic capacitor increases. Figure 4 shows the DC bias characteristics (by Murata Manufacturing Co.).

Example: Characteristic of Ceramic Capacitor (make: Murata Manufacturing Co.)

GRM32ER7YA106KA12 10µF±10%, 35V, X7R 100 10

fSW = 1MHz 0.5 Rated voltage 0

) ℃ -10

-20

10 -30

CAP. CHANGE (%) CHANGE CAP. -40

( RISE TEMPERATURE -50

1 -60 0 1 2 3 4 5 6 7 0 10 20 30 40 CURRENT (A) DC BIAS (V)

Figure 3. Ripple heat generation characteristic Figure 4. DC bias characteristic

Input ripple voltage of regulator is decided by the value of input capacitance. Input ripple voltage ΔVIN can be calculated by the following equation.

푉푂푈푇 (1 − ) × 퐼푂(푀퐴푋) × 푉푂푈푇 푉퐼푁 푉푂푈푇 Δ푉퐼푁 = + (1 − ) × 퐼푂(푀퐴푋) × 퐸푆푅푀퐴푋 [VP−P] (2) 퐶퐼푁 × 푓푆푊 × 푉퐼푁 푉퐼푁

푉퐼푁: Input voltage [V]

푉푂푈푇: Output voltage [V]

퐼푂(푀퐴푋): Maximum load current [A]

퐶퐼푁: Input capacitor [F]

푓푆푊: Switching frequency [Hz]

퐸푆푅푀퐴푋: Maximum equivalent series resistance ESR [Ω] of input capacitor

Calculation example of input capacitor For this design example, parameters listed in Table1 will be used. As for the input capacitor, Murata Manufacturing Co. make10µF / 35V ceramic capacitor is considered for reference.

Parameter Value

Input voltage range VIN 7V to 28V

Output voltage VOUT 3.3V

Input ripple voltage ΔVIN 300mV

Output ripple voltage ΔVO 33mV (1% of output voltage)

Output rating current IO 3A

Inductor ripple current ΔIL 0.9A (30% of output rating current)

Operation frequency fSW 1MHz

Table1. Design parameter

Calculate input ripple current by substituting each parameter to the equation (1).

푉푂푈푇 2 푉푂푈푇 1 2 3.3 2 3.3 1 2 퐼퐶퐼푁 = √ {퐼푂 (1 − ) + ∆퐼퐿 } = √ {3 (1 − ) + × 0.9 } = 1.508 [ARMS] (3) 푉퐼푁(푀퐼푁) 푉퐼푁(푀퐼푁) 12 7 7 12

From Figure 3 ripple current capacitance obtains enough margins.

Next, calculate input ripple voltage by substituting each parameter to equation (2). At this point consideration for DC bias characteristic of ceramic capacitor is necessary. In this example, since the maximum voltage impressed to capacitor is 28V, 48% will be reduced from rating capacitance value as from Figure 4. Also, ESR of ceramic capacitor is 2mΩ.

푉푂푈푇 (1 − ) × 퐼푂(푀퐴푋) × 푉푂푈푇 푉퐼푁 푉푂푈푇 Δ푉퐼푁 = + (1 − ) × 퐼푂(푀퐴푋) × 퐸푆푅푀퐴푋 [VP−P] 퐶퐼푁 × 푓푆푊 × 푉퐼푁 푉퐼푁

3.3 (1− )×3×3.3 3.3 = 28 + (1 − ) × (3 × 2 × 10−3) = 65.3 [mV ] (4) (10×10−6×0.52)×1×106×28 28 P−P

Ripple voltage of minimum input voltage can be shown as below method.

3.3 (1− )×3×3.3 7 3.3 −3 ∆푉 = + (1 − ) × (3 × 2 × 10 ) = 81.0 [mV ] (5) 퐼푁 (10×10−6×0.96)×1×106×7 7 P−P

The design requirement for input ripple voltage below 300mV can be confirmed. Maximum voltage at both ends of input capacitor is

VIN(MAX) + ΔVIN/2. To obtain more voltage margins, give consideration of using two 4.7µF / 50V capacitors in parallel. Also, be cautious for actual input ripple voltage that may get higher than the calculated value, due to output impedance of the voltage source (preceding circuit) and parasitic component resulting from the PCB layout.

Calculation of output capacitor

Important elements in designing output capacitor are rating voltage, ripple rating current, and ESR (equivalent series resistance). Ripple current and voltage impressed to the capacitor must be less than the maximum rating. ESR is an important element to decide the output ripple voltage with the inductor current.

The effective value of ripple current, the alternating component included in the output current, can be calculated by the following equation as it is a triangular waveform like ICO of Figure 2.

1 푉푂푈푇(푉퐼푁(푀퐴푋)−푉푂푈푇) 퐼퐶푂 = × [ARMS] (6) √12 퐿×푓푆푊×푉퐼푁(푀퐴푋)

푉퐼푁(푀퐴푋): Maximum input voltage [V]

푉푂푈푇: Output voltage [V] 퐿 : Inductor value [H]

푓푆푊: Switching frequency [Hz]

Output ripple voltage is the composite waveform created by the ripple current of the inductor flowing through the output capacitor depending on electrostatic capacitance, ESR, and ESL. It can be calculated by the following equation.

1 푉퐼푁(푀퐴푋) ∆푉푂푅푃퐿 = ∆퐼퐿 ( + 퐸푆푅) + 퐸푆퐿 [VP-P] (7) 8×퐶푂×푓푆푊 퐿

푉퐼푁(푀퐴푋): Maximum input voltage [V]

∆퐼퐿: Inductor ripple current [A]

퐶푂: Output capacitor [F] 퐿 : Inductor value [H]

푓푆푊: Switching frequency [Hz] ESR: Equivalent series resistor of output capacitor [Ω] ESL: Equivalent series inductor of output capacitor [H]

When using leaded type aluminum electrolytic capacitor with high ESR and ESL as an output capacitor, notice that ripple by ESR and ESL may get bigger than the ripple by capacitance.

Calculation example of output capacitor

For this design example, parameters listed in Table 1 will be used. As for the input capacitor, Murata Manufacturing Co. make 22µF / 25V ceramic capacitor is considered as reference. Calculate ripple current by substituting each parameter to equation (6). Use 4.7µH value for coil L.

1 푉푂푈푇(푉퐼푁(푀퐴푋)−푉푂푈푇) 1 3.3(28−3.3) 퐼퐶푂 = × = × −6 6 = 0.18 [ARMS] (8) √12 퐿×푓푆푊×푉퐼푁(푀퐴푋) √12 4.7×10 ×1×10 ×28

From Figure 5 ripple current capacitance obtains enough margin.

Next, calculate output ripple voltage by substituting each parameter to equation (7). At this point consideration for DC bias characteristic of ceramic capacitor is necessary. In this example, because the voltage impressed to capacitor is 3.3V, 2% will be reduced from rating capacitance value as in Figure 6. Also, ESR of ceramic capacitor is 2mΩ and ESL is 0.4nH.

1 푉퐼푁(푀퐴푋) ∆푉푂푅푃퐿 = ∆퐼퐿 ( + 퐸푆푅) + 퐸푆퐿 8×퐶푂×푓푆푊 퐿

1 −3 −9 28 = 0.9 ( + 2 × 10 ) + 0.4 × 10 ( ) = 9.4 [mVP-P] (9) 8×(22×10−6×0.98)×1×106 4.7×10−6

Output ripple voltage requirement is 33mV, meaning that the above value satisfies. But, the actual output ripple voltage can be influenced by ESR, ESL elements of capacitor and by parasitic element originated in PCB layout, causing difference from the calculated value.

Example: Characteristic of Ceramic Capacitor (make: Murata Manufacturing Co.) GRM32ER71E226ME15 22µF±20%, 25V, X7R

100 10

fSW = 1MHz 0 0.5 Rated voltage

) -10 ℃ -20

-30

10 -40

-50

-60

(%) CHANGE CAP. -70 TEMPERATURE ( RISE -80

1 -90 0 1 2 3 4 5 6 7 0 10 20 30 CURRENT (A) DC BIAS (V) Figure 5. Ripple heat generation characteristic Figure 6. DC bias characteristic

Equation of buck converter

푉퐼푁: Input voltage [V] ・Effective value of ripple current flowing in input capacitor 푉퐼푁(푀퐼푁): Minimum input voltage [V]

푉푂푈푇: Output voltage [V] 푉푂푈푇 푉푂푈푇 1 2 2 퐼푂: Output rating current [A] 퐼퐶퐼푁 = √ {퐼푂 (1 − ) + ∆퐼퐿 } [ARMS] 푉퐼푁(푀퐼푁) 푉퐼푁(푀퐼푁) 12 ∆퐼푂: Inductor ripple current [A]

(Usually set between 20% and 50% of IO)

퐼푂(푀퐴푋): Maximum load current [A] ・Input ripple voltage 퐶퐼푁: Input capacitor [F]

푉푂푈푇 푓푆푊: Switching frequency [Hz] (1 − ) × 퐼푂(푀퐴푋) × 푉푂푈푇 푉퐼푁 푉푂푈푇 Δ푉퐼푁 = + (1 − ) × 퐼푂(푀퐴푋) × 퐸푆푅푀퐴푋 [VP−P] 퐸푆푅푀퐴푋: Maximum equivalent series resistance 퐶퐼푁 × 푓푆푊 × 푉퐼푁 푉퐼푁 of Input capacitor [Ω]

IIN IDD

1 ICIN Q ON IL L IO OFF

VIN CIN

ID ICO

D CO RL VOUT

Buck converter

・Effective value of ripple current flowing in output capacitor 푉퐼푁(푀퐴푋): Maximum input voltage [V] 푉 : Output voltage [V] 1 푉푂푈푇(푉퐼푁(푀퐴푋) − 푉푂푈푇) 푂푈푇 퐼퐶푂 = × [ARMS] √12 퐿 × 푓푆푊 × 푉퐼푁(푀퐴푋) 퐿 L: Inductor value [H]

푓푆푊: Switching frequency [Hz]

∆퐼퐿: Inductor ripple current [A] ・Output ripple voltage (Usually set between 20% and 50% of IO) 퐶 : Output capacitor [F] 1 푉퐼푁(푀퐴푋) 푂 ∆푉푂푅푃퐿 = ∆퐼퐿 ( + 퐸푆푅) + 퐸푆퐿 [VP−P] 8 × 퐶푂 × 푓푆푊 퐿 ESR: Equivalent series resistance of output capacitor [Ω] ESL: Equivalent series inductance of output capacitor [H]

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